Optimization of Connectivity in WSN using Fuzzy Logic

Lu Peng, Shannon Tao and Vivian Yang

Table of Contents Introduction .............................................................................................................................. 2

Theoretical bases and literature review ................................................................................... 3

Hypothesis ................................................................................................................................ 7

Methodology ............................................................................................................................. 7

Generate/collect data ........................................................................................................... 7

How to solve problem ........................................................................................................... 7

Algorithm .......................................................................................................................... 8

Language ......................................................................................................................... 11

Tool ................................................................................................................................. 11

Generate output ................................................................................................................. 12

Test against hypothesis ....................................................................................................... 12

Implementation ...................................................................................................................... 13

Code (see attachment) ....................................................................................................... 13

Design document and flow chart ........................................................................................ 13

Data analysis ........................................................................................................................... 14

Output generation: ............................................................................................................. 14

Case 1 with fairly large improvement ............................................................................. 14

Case 2 with a small improvement ................................................................................... 21

Case 3 with no improvement .......................................................................................... 27

Fuzzy logic control has a positive impact on WSN packet transmission............................. 33

Fuzzy logic control has a positive impact on WSN energy utilization ................................. 36

Conclusion ............................................................................................................................... 38

Recommendation for Future Studies ...................................................................................... 38

Bibliography ............................................................................................................................ 39

Appendix ................................................................................................................................. 43

Introduction

Wireless sensor network (WSN)[1][2] is a promising technology nowadays. It is used in

numerous applications, such as forest monitoring, disaster management, space exploration,

factory automation, secure installation, border protection, battlefield surveillance, etc., and is the

basis of future network “Internet of Things” (IoT)[3]. A WSN is composed of spatially scattered

sensor nodes over a certain region to monitor a certain number of tasks. The sensor nodes are

positioned near to the target they are monitoring. The sensors correspond with one or more

central positions, normally called base station or a sink. The more modern networks are bi-

directional, also enabling control of sensor activity. A distinct sensor node contains a logic unit, a

process unit to execute computations, a radio unit to unite nodes to the system and a battery

power unit. Due to lack of regular power source of sensor nodes, energy preservation become the

major difference between WSN and other wireless networks, and draw most attention in

algorithms and protocols development.

A great challenge in this new field is achieving a global coordinated objective while using

only local information [4]–[17]. Maintaining connectivity has become one of the most important

and challenging task in WSN control [18]–[29]. When designing, deploying and exploiting a

WSN, it is desired to maximize the number of nodes that are able to transmit or receive data to or

from the base station (BS), considering the BS as an element in the network acting as a gateway

between the WSN and any other data networks. Unfortunately, the number of connected nodes in

a WSN (nodes that are able to send or receive data to or from the BS) would decrease over time

as nodes relaying messages crash or fail due to hardware failures, battery discharge, software

bugs and so forth.

There are several approaches and strategies that will minimize such risks and will improve

the WSN connectivity. Most of them are high resource consuming as nodes are checking their

availability of reaching a BS from time to time. The network is flooded with control messages

that impact negatively on the performance and the energy efficiency of all the nodes in the path.

One of the approaches provides a better trade-off between the network connectivity and the

resource consumption, which will be adopted in our project as a starting point, on top of which a

fuzzy logic based connectivity control will be carried out to further improve the performance. In

order to better understand the effect of fuzzy logic function on this issue, different functions will

be implemented and compared, and the one with the best result will be shown to guide future

direction in the field.

Theoretical bases and literature review

Cooperative control of multi-agent systems is a very active research area of control theory. In

the past few years problems such as flocking, consensus, coverage and pattern formation have

been studied. The study is generally focused on the development of distributed control laws in

order to reach a global objective [1]–[7]. One interesting problem recently analyzed regards the

connectivity maintenance of the distance-dependent graph of the network. In such a graph, known

also as R-disk graph [7], there is an edge between two nodes if their Euclidean distance is less

than or equal to a pre specified number R. In such a graph, known also as R-disk graph [30], there

is an edge between two nodes if their Euclidean distance is less than or equal to a pre specified

number R. The difficulty in connectivity maintenance stems from the fact that connectivity is an

inherently global property and a complicated function of the motion of the nodes. Other attempts

to model changes in topology, such as [31], ignore the dependence of switching on motion.

Several attempts have been made in the wireless networking literature to follow local rules that

guarantee connectivity. One example is the “sector rule” which guarantees connectivity of the R-

disk graph on the plane if each agent has at least one neighbor in every sector of 120 degrees [32].

Another interesting solution to the connectivity problem is given by the circumcenter algorithm,

which increases gradually the degree of each agent and constraints the motion of the agents to

avoid the lost of previously present connections [30]. Many authors in the control theory

literature have also made progress on this problem [33]–[36].

The strategy in our project aims at keeping constant the node degree (ND) of a node, its

number of neighbors. The node degree depends on the WSN deployment (regular, random, etc.),

the area to be covered and the number of nodes. So, the desired node degree will be calculated for

the specific WSN to be deployed and that value will become the target of the self-adaptive system.

The average degree should not be too large because a large degree typically implies that a node

has to communicate with other distant nodes directly. This increases interference and collision,

and would waste energy. The average degree should not be too small either because that tends to

increase the overall network energy consumption as longer paths have to be taken. So we believe

the average node degree is an important performance metric for multihop wireless network

topology. Intuitively, if a node has a higher degree (indicates more neighbors), it is more likely

that there are at least one path for it to transmit data to the destination. If all nodes are randomly

and uniformly deployed, the probabilistic approach to analyze the relation between the node

degree and the network connectivity is fully described in [37].

The self-adaptive system presented here aims to control the communication range of each

node to manage its degree, in order to recover the link when its neighbors fail. Whenever a node’s

neighbor fails, the communication range of that node is increased to replace the failing neighbor.

Therefore the node’s energy consumption is likely to increase. If the desired node degree, whose

value is estimated before the nodes deployment as mentioned above, is kept constant all the time,

the battery might become exhausted too short. Thus, the desired node degree has to be adjusted in

run time taking into account the battery level and the desired lifetime of autonomous nodes. Note

that directly changing communication range usually is not feasible, instead the transmission

power is the parameter can be controlled in real sensor nodes. In this paper, we employed the

transmission power model in the literature [38], in which the transmission power is linear

function of square of the communication range.

The basic idea of the control system is that if the node degree is higher than the expected

node degree, then the communication range has to be decreased; if the node degree is lower than

the expected node degree, then the communication range has to be increased. The desired node

degree will depend on the energy of the node. How fast and how long the communication range

changes, is decided by the controller, e.g. fuzzy logic based controller.

First we need to understand what exactly is fuzzy logic. Fuzzy logic is a form of many-valued

logic which deals with reasoning that is approximate rather than fixed and exact. Fuzzy logic has

two different meanings. In a narrow sense, fuzzy logic is a logical system, which is an extension

of multivalued logic. However, in a wider sense fuzzy logic (FL) is almost synonymous with the

theory of fuzzy sets, a theory which relates to classes of objects with unsharp boundaries in which

membership is a matter of degree. In this perspective, fuzzy logic in its narrow sense is a branch

of FL. Even in its more narrow definition, fuzzy logic differs both in concept and substance from

traditional multi valued logical systems[39].

Another basic concept in FL, which plays a central role in most of its applications, is that of a

fuzzy if-then rule or, simply, fuzzy rule. Although rule-based systems have a long history of use

in Artificial Intelligence (AI), what is missing in such systems is a mechanism for dealing with

fuzzy consequents and fuzzy antecedents. In fuzzy logic, this mechanism is provided by the

calculus of fuzzy rules. The calculus of fuzzy rules serves as a basis for what might be called the

Fuzzy Dependency and Command Language (FDCL). Although FDCL is not used explicitly in

the toolbox, it is effectively one of its principal constituents. In most of the applications of fuzzy

logic, a fuzzy logic solution is, in reality, a translation of a human solution into FDCL.

First fuzzy logic composed of Membership Functions(MF) which is a curve that defines how

each point in the input space is mapped to a membership value (or degrees of membership)

between 0 and 1. For example, when we define somebody is tall, we don’t have a clear boundary

between above which height is considered tall. We only have a rough idea of the definition of tall.

In this case we can only use curve instead of linear lines to represent the tallness. As described in

Fig 1 and 2, it’s obviously more sensible to define tall in the curve format. When someone is 5 ft

9 inches, we can say he is tall to the degree of 0.7. And we can map these values accordingly on

to the curve function.

Figure1. Linear function to define tallness

Figure2. curve to define tallness

The second component of fuzzy logic is the If-Then rules. Fuzzy sets and fuzzy operators are

the subjects and verbs of fuzzy logic. These if-then rule statements are used to formulate the

conditional statements that comprise fuzzy logic.

The simple format of fuzzy if-then rule is :

● if x is A then y is B.

where A and B are linguistic values defined by fuzzy sets on the ranges X and Y. Taken our

previous example on the tallness, we can define a if-then rule as “If a man is 5 ft. 9 inches, then

he is tall with a degree of 0.7. In general, the input to an if-then rule is the current value for the

input variable and the output is an entire fuzzy set[40] .

The last component is the fuzzy inference. Fuzzy inference is the process of formulating the

mapping from a given input to an output using fuzzy logic[41] . The mapping then provides a

basis from which decisions can be made, or patterns discerned. The process of fuzzy inference

involves all of the pieces that are described in Membership Functions, Logical Operations, and If-

Then rules. We take the inputs and determine the degree to which they belong to each of the

appropriate fuzzy sets via membership functions. The output is a fuzzy degree of membership in

the qualifying linguistic set which always are the intervals between 0 and 1.We also need to

aggregate all outputs in order to make decisions based on the results. Aggregation is the process

by which the fuzzy sets that represent the outputs of each rule are combined into a single fuzzy

set. Lastly is the defuzzify process. The input for the defuzzification process is a fuzzy set (the

aggregate output fuzzy set) and the output is a single number which is the result we want to

derive from the fuzzy inference process.

Hypothesis

There are several approaches and strategies that will minimize the risks of message delaying

fails, and thus improve WSN connectivity. However most of them will require high power

consumption since each node is actively checking others’ availability of reaching the BS. We aim

to tackle both problems of poor connectivity and also to save power by using the fuzzy logic

controller on each node to monitor the node’s own parameters, without flooding WSN with

monitoring messages. We use control loops based on fuzzy logic to enable each node to adjust

automatically the communication range according to a desired node degree and residual energy.

Methodology

Generate/collect data

a. The base station is positioned at the center of the 100 * 100 area

b. Generate 30 random sensor nodes in the area and initialize every node with a random

communication range within a given range (10 to 30).

c. Other strategies to initialize the network: 1). deploy the nodes semi-randomly by fixing

each node within a certain area; 2). initialize the communication range with a constant

d. In each cycle, update the status of every node and then transmit a packet from each node

to base station(success or fail) and count

How to solve problem

Algorithm

The algorithm contains three loops: main loop, primary loop, secondary loop (Figure

1)

i. Main loop: update the whole system

Update the status of every node

Calculate the paths from sensor nodes to base station (undirected and weighted graph)

Monitor the packet transmission from sensor nodes to base station

Do analysis of the whole system and display and update the result.

Figure 1. Flow chart of fuzzy-logic based control system

ii. Primary loop: update each node of its communication range

Inputs: current energy level and node degree of a node, and a set of predefined

parameters including:

initial value of the communication range ( 𝐶𝑅0̅̅ ̅̅ ̅ ); desired value of the

node degree when the battery has a critical energy level (𝑁𝐷̅̅ ̅̅ ); critical energy level

(𝐸𝑐𝑟̅̅ ̅̅ ); communication range variation rate (Δcr̅̅̅̅̅); node degree variation rate (Δnd̅̅ ̅̅ ̅);

minimum and maximum value of the communication range (CRmin and CRmax).

Loop: input modification and normalization, and fuzzy-logic based function of

decision making

(1) Membership functions: for comparison, two configurations, trapezoidal-

triangle mixed shape (Figure 2) and triangle-shape (Figure 3) are used to

evaluate the normalized changes (e) of node degree

𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 − 𝑠ℎ𝑎𝑝𝑒 𝜇(𝑥) =

{

0, 𝑥 ≤ 𝑎; 𝑥 ≥ 𝑐

𝑥 − 𝑎

𝑏 − 𝑎, 𝑎 ≤ 𝑥 ≤ 𝑏

𝑐 − 𝑥

𝑐 − 𝑏, 𝑏 ≤ 𝑥 ≤ 𝑐

𝑡𝑟𝑎𝑝𝑒𝑧𝑜𝑖𝑑𝑎𝑙 − 𝑠ℎ𝑎𝑝𝑒 𝜇(𝑥) =

{

0, 𝑥 ≤ 𝑎; 𝑥 ≥ 𝑑

𝑥 − 𝑎

𝑏 − 𝑎, 𝑎 ≤ 𝑥 ≤ 𝑏

1, 𝑏 ≤ 𝑥 ≤ 𝑐

𝑑 − 𝑥

𝑑 − 𝑐, 𝑐 ≤ 𝑥 ≤ 𝑑

(2) Input space is partitioned in three regions: negative values(NV), zero

values(ZV) and positive values(PV), and their corresponding output variable

(u) is:

∆𝑢 =

{

𝑓𝑁𝐶 = −1, 𝑒 ∈ 𝑁𝑉

𝑓𝑁𝐶 = 0, 𝑒 ∈ 𝑍𝑉

𝑓𝑁𝐶 = 1, 𝑒 ∈ 𝑃𝑉

regio

n

MF a b c d boundaries

NV 𝜇𝑁𝑉(𝑒) -4 -2 -0.5 0 𝑒 < 0

ZV 𝜇𝑍𝑉(𝑒) -0.5 0 0.5 −0.5 ≤ 𝑒 ≤ 0.5

PV 𝜇𝑃𝑉(𝑒) 0 0.5 2 4 𝑒 > 0

Table 1. Parameters of membership functions with mixed shape

Figure 2. Membership functions of trapezoidal-triangle mixed shape

regio

n

MF a b c boundaries

NV 𝜇𝑁𝑉(𝑒) -2 -1 0 𝑒 < 0

ZV 𝜇𝑍𝑉(𝑒) -1 0 1 −1 ≤ 𝑒 ≤ 1

PV 𝜇𝑃𝑉(𝑒) 0 1 2 𝑒 > 0

Table 2. Parameters of membership functions with triangle shape

Figure 3. Membership functions of triangle shape

0

0.2

0.4

0.6

0.8

1

1.2

-1 -0.5 0 0.5 1

µ(e)

e

NV ZV PV

0

0.2

0.4

0.6

0.8

1

1.2

-1 -0.5 0 0.5 1

µ(e)

e

NV ZV

PV

Outputs: normalized communication range variation factor which can be used to

calculate the updated communication range and update energy level after packet

transmission

iii. Secondary loop: update the desired node degree of each node using its battery level.

Same fuzzy-logic membership functions as the primary loop are used.

Language

We will implement the program in Java. The simulation and data analysis will be

visualized using Java GUI tools.

Tool

JFreeChart (http://www.jfree.org/jfreechart/)

Generate output

a. Draw the nodes network connected graph against time (cycle number) to display the

change in connectivity of the network.

b. Draw the shortest distance path from each sensor node to the based station to visualize

the packet transmission in each cycle.

c. Plot the total remaining energy of the system against time(cycle number)

d. Record the total number of packets received at based station

Test against hypothesis

a. Compare the network connection in each cycle and show the dynamic change of the

connected sensor network and the packet transmission paths.

b. Compare the number of packets received at based station of fuzzy-logic based system

with that of static non-fuzzy system to show the advantages of fuzzy-logic controlled

system

c. Compare numbers of packets transmitted using different fuzzy-logic functions to show

the choice of fuzzy-logic functions can affect the performance of sensor network

d. Compare the changes of total network energy between fuzzy-logic based and static

systems to show the different energy consumption footprints in these two types of

systems

Implementation

Code (see attachment)

Design document and flow chart

a. Generation of a list of nodes including a based station node and 30 random sensors nodes.

The newly generated list is saved to a txt file so that the same input data can be used for

simulations with and without fuzzy logic as well as different fuzzy-logic configurations.

b. To start the simulation, a list of nodes is either generated at will or imported from a txt

file, followed by the generation of the starting sensor network graph.

c. Before simulation, options for configurations can be selected: fuzzy-logic or non-fuzzy-

logic, fuzzy-logic configuration 1 or 2

d. In the main loop, at most 30 cycles of simulations are performed. In each cycle, the status

of each node (communication range) is updated by fuzzy-logic function using its battery

level and node degree. Then the new network graph and shortest path graph are

calculated, displayed and saved as a png file. The total remaining energy and number of

packets transmitted in each cycle are also saved for data analysis.

e. Shortest path graphs are calculated as single-drain shortest-path graphs

f. After the loop, the total number of packets transmitted in the simulation is displayed in

console, and a graph plotting the total remaining energy in each cycle is shown.

Data analysis

Output generation:

To study the influence of fuzzy-logic on the wireless sensor network performance, we

generate multiple sets of input data. And we compare the performance of WSN with three

different configurations: fuzzy-logic configuration 1, fuzzy-logic configuration 2 and non-

fuzzy-logic configuration. The specific parameters for comparison are: total packet received

at base station and total remaining energy of the network of each cycle. In general, based on

the number of packets transmitted, the data sets can be divided into three groups:

i. Cases with fairly large improvement

ii. Cases with a small improvement

iii. Cases with no improvement

Case 1 with fairly large improvement

List of nodes

Node Index x y CR

0 (base station) 50 50 0

1 98 33 24

2 50 12 25

3 6 93 19

4 29 10 25

5 41 36 11

6 96 53 10

7 85 97 28

8 15 39 13

9 84 40 26

10 21 90 21

11 55 87 19

12 71 4 18

13 34 37 19

14 31 9 29

15 67 11 12

16 21 20 15

17 55 14 11

18 52 30 25

19 76 52 15

20 27 93 18

21 99 96 26

22 5 42 22

23 9 64 27

24 69 10 25

25 27 57 17

26 2 40 12

27 8 93 14

28 60 63 20

29 60 97 29

30 87 77 25

WSN network graph before simulation

In the graph, the green dots are sensor nodes and black dot in the center is the

base station. The arrowed lines indicate a directed connection from one node to

another.

Simulation without fuzzy-logic based control

The left pictures are connected graphs of the network and right pictures are calculated

shortest path graph. As we can see from the graphs, the basic structure of the WSN connection

graph (shown in left pics) does not change. The only change is that as time goes by, some of the

connections are broken due to the depletion of energy of some nodes (red dots). Meanwhile, the

calculated shorted paths exhibit similar change. Because communication range of every node is

fixed, no new connection can be formed after some of the nodes lose power.

Cycle #1

Cycle #15

Cycle #26

Dynamic changes of WSN network and shortest path graphs

Different from the behavior of the static WSN network, both the left and right graphs

changes as simulation continues. This shows that the WSN controlled by fuzzy logic can

dynamically adjust its connection and the shortest path graph, due to the fact that every

node can change its communication range through fuzzy-logic feedback system using its

current energy level and node degree.

Fuzzy logic configuration 1

Cycle #1

Cycle #4

Cycle #7

Fuzzy logic configuration 2

The simulation result is almost the same as that of fuzzy logic configuration 1.

Cycle #1

Cycle #4

Cycle #7

Footprint of total WSN energy

As we can see from the graphs, in simulation without fuzzy-logic, the total

energy of the WSN network decreases by a small percentage followed by a plateau.

The shape of the curve shows after the initial packet transmission, no signification

further transmission is observed, which means in real WSN system, the data

collection at base station is stopped and WSN loses its function. In comparison, the

system with fuzzy logic control keeps consuming energy and transmitting packets to

base station even when a significant percentage of the energy is consumed. So this

type of WSN is able to collect more data and make better use of its resources.

Non-fuzzy logic Fuzzy logic config. 1

Fuzzy logic config. 2

Total number of packets transmitted in simulation

Non-fuzzy

logic

Fuzzy-logic config.

1

Fuzzy-logic config.

2

Number of packets 43 120 120

Case 2 with a small improvement

The chance of getting this type of cases in random generation of nodes are lower than the

case 1. In this case, the improvement of packet transmission is small, although the fuzzy-logic

controlled system still shows dynamic changing in connection graph and shortest path graph.

List of nodes

Node Index x y CR

0 (base station) 50 50 0

1 67 20 29

2 73 27 12

3 93 67 28

4 90 65 13

5 51 82 23

6 78 70 17

7 10 14 27

8 35 15 19

9 62 43 17

10 89 37 23

11 58 52 28

12 55 47 23

13 81 1 21

14 9 57 12

15 76 13 19

16 58 85 10

17 99 6 27

18 26 84 13

19 67 19 21

20 63 62 13

21 86 45 18

22 36 49 28

23 27 19 15

24 8 97 22

25 29 59 15

26 7 80 24

27 7 78 26

28 6 25 12

29 78 79 19

30 60 18 27

WSN network graph before simulation

In the graph, the green dots are sensor nodes and black dot in the center is the

base station. The arrowed lines indicate a directed connection from one node to

another.

Simulation without fuzzy-logic based control

Cycle #1

Cycle #11

Cycle #21

Dynamic changes of WSN network and shortest path graphs

Fuzzy logic configuration 1

Cycle #1

Cycle #4

Cycle #7

Fuzzy logic configuration 2

The simulation result shows dynamic change of graph but is different from that of fuzzy

logic configuration 1.

Cycle #1

Cycle #5

Cycle #10

Footprint of total WSN energy

Behavior is similar to that in case 1

Non-fuzzy logic Fuzzy logic config. 1

Fuzzy logic config. 2

Total number of packets transmitted in simulation

Non-fuzzy

logic

Fuzzy-logic

config. 1

Fuzzy-logic

config. 2

Number of

packets

87 133 120

Case 3 with no improvement

The chance of getting this type of cases in random generation of nodes are lower than the

case 1 and 2. In this case, the improvement of packet transmission is not obvious, and the

fuzzy-logic controlled system doesn’t show obvious dynamic changing in connection graph

and shortest path graph.

List of nodes

Node Index x y CR

0 (base station) 50 50 0

1 94 73 21

2 47 89 29

3 95 98 19

4 30 84 15

5 51 50 13

6 90 35 11

7 45 90 25

8 42 9 11

9 0 90 17

10 94 31 26

11 73 96 20

12 7 16 29

13 54 36 25

14 56 49 16

15 10 16 18

16 62 5 14

17 97 22 22

18 76 96 24

19 91 5 19

20 77 35 21

21 68 79 10

22 95 28 11

23 69 25 22

24 32 20 13

25 59 89 12

26 17 29 20

27 87 35 13

28 56 87 29

29 71 88 15

30 34 76 25

WSN network graph before simulation

In the graph, the green dots are sensor nodes and black dot in the center is the

base station. The arrowed lines indicate a directed connection from one node to

another.

Simulation without fuzzy-logic based control

Cycle #1

Cycle #15

Cycle #30

Dynamic changes of WSN network and shortest path graphs

Fuzzy logic configuration 1

The shortest path is similar to that of non-fuzzy logic system. As the energy of

the node consumes, the shortest path graph does not change much compared with the

previous 2 cases which mean this sensor nodes system has flawed initial state which

restricts its dynamic properties.

Cycle #1

Cycle #8

Cycle #16

Fuzzy logic configuration 2

The simulation result is similar to that of fuzzy logic configuration 1.

Cycle #1

Cycle #8

Cycle #16

Footprint of total WSN energy

All three configurations show similar curve of energy in each cycle. At the

end of simulation, all three still have a large percentage of energy left in the

system, which means the WSN network does not functions well . And the data

collected in the course is very limited.

Non-fuzzy logic Fuzzy logic config. 1

Fuzzy logic config. 2

Total number of packets transmitted in simulation

Non-fuzzy

logic

Fuzzy-logic

config. 1

Fuzzy-logic

config. 2

Number of

packets

60 47 78

i. In above special case, the improvement based on fuzzy logic is not significant.

However there are a few observations that we made:

In the connectivity graph, one critical node in the topology has run out of power. The

network without fuzzy logic will immediately get disconnected, no more packets are sent

to the Base Station anymore. However, for the network with fuzzy logic, the

communication range of nodes automatically get adjusted to increase the node degree. As

a result, new path has been identified and new connection has been established.

In terms of the shortest path tree, once the critical node run out of power, the shortest

path will be destroyed because of the disconnect. For the network with fuzzy logic, since

connectivity graph has been dynamically established, new shorted path has been created.

To some example, the new shorted path performs even better than the old shorted path.

For the energy left analysis, because of the disconnect, the network without fuzzy logic

will stop consuming power and the total power displays a horizontal line with no

reduction. This proves to be very inefficient since most of the nodes are still fully charged.

This demonstrates that the power utilization is highly dependent on the topology of the

network, which in turn suggests that the topology can become a bottleneck for the entire

network. However one of the most important feature of Wireless Sensor Network is the

randomly distributed nodes. In contrast, the network with fuzzy logic shows better

utilization of the node power. Even though in the chart the curve becomes flat as time

goes by, but still more power are consumed before that which means more nodes served

their job.

Fuzzy logic control has a positive impact on WSN packet

transmission

In order to measure the network performance, the total number of packets received at base

station during the whole simulation has been measured. For each fuzzy control function, 100

different network topologies have been simulated. The nodes for each network are randomly

deployed and the simulation has been executed three times: without the fuzzy control-based

algorithm, with fuzzy control using our first fuzzy function, and with fuzzy control using our

second fuzzy function. The raw data is shown in Appendix Table I where the first column is the

total number of packets transmitted when no fuzzy control is used (PBS_NC). This is our

experimental control. The second column is the number of packets transmitted (PBS_WC1) and the

percentage increase when using the first fuzzy logic control function. The third column is the

number of packets transmitted (PBS_WC2) and the percentage increase when using the second fuzzy

logic control function. The percentage increase is calculated as 100% x (PBS_WC - PBS_NC) / PBS_NC.

To further analyze the data, improvement histograms are made and shown in Figure I and

II. Upon calculation, it is found that the first fuzzy logic control function has an impact of an

average of 77.11% improvement in the total number of packet transmission with a standard

deviation of 72.71%, whereas the second fuzzy logic control function has 75.57% mean value and

72.75% standard deviation.

After an analysis of the results, the following observations can be made: (1) in general, more

packages were received at BS when the fuzzy control algorithm was applied; (2) the two fuzzy

logic control function have similar impact on the system performance with the first function

performing slightly better; (3) in general the self-adaptive communication range based on fuzzy

control loops improves the connectivity of the network.

Figure I. Number of packet improvement percentage histogram of 100 randomly

deployed networks with the first fuzzy logic control function.

Figure II. Number of packet improvement percentage histogram of 100 randomly

deployed networks with the second fuzzy logic control function.

Fuzzy logic control has a positive impact on WSN energy utilization

Similar to the packet transmission, 100 topologies were used to calculate the energy

consumption statistically. The result is shown in Appendix Table II. E0 is the initial energy of the

whole network. EBS_NC, EBS_WC1, and EBS_WC2 are energy leftover and leftover percentage

compared to E0 either with no fuzzy function, with the first fuzzy function, or with the second

fuzzy function, respectively. Energy leftover percentage histograms are made and shown in

Figure III, IV and V. As can be seen from the figure, if no fuzzy control is used, the network

become paralyzed when there is still about 80% energy left in the system. However, if fuzzy

control is applied, because of the improvement in the network connectivity, the total energy of the

system can be better utilized and drop the leftover energy to about 40%. This means the energy

utilization is doubled under fuzzy control. Energy consideration is known to be the most

important criteria in handling WSN, our result has indicated that fuzzy control can greatly

improve the energy utilization and thus system performance, resulting in a much better WSN

connectivity control manipulation.

Figure III. Energy leftover percentage histogram of 100 randomly deployed networks

without using fuzzy logic control.

Figure IV. Energy leftover percentage histogram of 100 randomly deployed networks

with the first fuzzy logic control function.

Figure V. Energy leftover percentage histogram of 100 randomly deployed networks

with the second fuzzy logic control function.

Conclusion

The self-adaptive Wireless Sensor Network (WSN) based on Fuzzy Logic enables the nodes

to automatically adjust the communication range in order to increase / decrease the node degrees

(ND) of each node. This will directly improve the routing path of the packets to be delivered to

the desired destination. In addition, the adjustment of the communication range is taken into

consideration of the critical energy level of the individual node for the sake of energy saving. In

our paper we have proved that the total number of packets received by the Base Station have been

increased significantly comparing to the network without fuzzy logic. Also, the energy has been

better utilized. In our experiment , we’ve proven that the topology of the node distribution is

critical in the WSN, however by applying fuzzy logic, it won’t become a bottleneck which is the

case for the network without fuzzy logic. In conclusion, the network connectivity has been

improved and therefore the network is more resilient to the nodes failure.

Recommendation for Future Studies

During our research and experiment, we learnt that there are still several questions that are

still open. We’ve proven that the energy has been better utilized, but we didn’t derive any result

to prove the fuzzy logic can save more energy than without fuzzy logic. What’s the optimal

values for the fuzzy function parameters in order to achieve optimal balance between the

performance of the network connectivity and the energy consumption. Also what’s the optimal

algorithms to follow for various network topologies? How to adjust the desired node degree for

each node independently according to its location in the network? If we take into consideration of

other environmental factors like weather, humidity that will influence the network, what’s the

effect to our fuzzy logic functions. We hope all of these questions will be answered in future

works.

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Appendix

Trial E0 EBS_NC

NC

Leftover

Percentage

EBS_WC1

WC1

Leftover

Percentage

EBS_WC2

WC2

Leftover

Percentage

1 30000 17912 59.71% 8036 26.79% 9833 32.78%

2 30000 27402 91.34% 19662 65.54% 22261 74.20%

3 30000 23049 76.83% 20053 66.84% 20296 67.65%

4 30000 25398 84.66% 11404 38.01% 11553 38.51%

5 30000 27069 90.23% 18487 61.62% 16915 56.38%

6 30000 22274 74.25% 12219 40.73% 12990 43.30%

7 30000 19738 65.79% 5072 16.91% 4572 15.24%

8 30000 22041 73.47% 10006 33.35% 7089 23.63%

9 30000 17337 57.79% 6933 23.11% 6363 21.21%

10 30000 16405 54.68% 6716 22.39% 8446 28.15%

11 30000 24096 80.32% 5382 17.94% 4725 15.75%

12 30000 21717 72.39% 10763 35.88% 15586 51.95%

13 30000 16916 56.39% 6464 21.55% 8160 27.20%

14 30000 26976 89.92% 10198 33.99% 11897 39.66%

15 30000 18932 63.11% 9198 30.66% 9649 32.16%

16 30000 17980 59.93% 6682 22.27% 6804 22.68%

17 30000 19328 64.43% 3375 11.25% 3235 10.78%

18 30000 17866 59.55% 4532 15.11% 4566 15.22%

19 30000 17730 59.10% 10120 33.73% 9290 30.97%

20 30000 21657 72.19% 8339 27.80% 9234 30.78%

21 30000 21750 72.50% 7252 24.17% 5171 17.24%

22 30000 25398 84.66% 8372 27.91% 12286 40.95%

23 30000 18678 62.26% 8333 27.78% 8369 27.90%

24 30000 19523 65.08% 3975 13.25% 6459 21.53%

25 30000 23381 77.94% 8445 28.15% 9836 32.79%

26 30000 21755 72.52% 11908 39.69% 9267 30.89%

27 30000 21942 73.14% 7727 25.76% 11296 37.65%

28 30000 26726 89.09% 6831 22.77% 6885 22.95%

29 30000 17067 56.89% 8736 29.12% 11334 37.78%

30 30000 23887 79.62% 8536 28.45% 7573 25.24%

31 30000 18156 60.52% 8254 27.51% 5623 18.74%

32 30000 29160 97.20% 14033 46.78% 14308 47.69%

33 30000 26514 88.38% 14337 47.79% 13073 43.58%

34 30000 24001 80.00% 8293 27.64% 8571 28.57%

35 30000 22618 75.39% 4692 15.64% 4040 13.47%

36 30000 25086 83.62% 11093 36.98% 10784 35.95%

37 30000 24358 81.19% 11252 37.51% 13768 45.89%

38 30000 21719 72.40% 7590 25.30% 7186 23.95%

39 30000 19784 65.95% 12211 40.70% 13262 44.21%

40 30000 22665 75.55% 9982 33.27% 10283 34.28%

41 30000 20387 67.96% 8766 29.22% 6725 22.42%

42 30000 22236 74.12% 20311 67.70% 18233 60.78%

43 30000 26780 89.27% 9408 31.36% 12979 43.26%

44 30000 20159 67.20% 14925 49.75% 18019 60.06%

45 30000 15993 53.31% 6894 22.98% 3463 11.54%

46 30000 20272 67.57% 5386 17.95% 4766 15.89%

47 30000 23810 79.37% 11293 37.64% 12753 42.51%

48 30000 20826 69.42% 7546 25.15% 8138 27.13%

49 30000 21694 72.31% 8142 27.14% 5791 19.30%

50 30000 21665 72.22% 8598 28.66% 7561 25.20%

51 30000 20412 68.04% 7408 24.69% 7913 26.38%

52 30000 26608 88.69% 17940 59.80% 13894 46.31%

53 30000 19398 64.66% 8145 27.15% 7569 25.23%

54 30000 22917 76.39% 7101 23.67% 16988 56.63%

55 30000 23861 79.54% 10286 34.29% 9945 33.15%

56 30000 22611 75.37% 5939 19.80% 6444 21.48%

57 30000 30000 100.00% 8024 26.75% 9503 31.68%

58 30000 26832 89.44% 7944 26.48% 6499 21.66%

59 30000 18419 61.40% 5265 17.55% 4881 16.27%

60 30000 21895 72.98% 9589 31.96% 9895 32.98%

61 30000 20639 68.80% 7313 24.38% 9176 30.59%

62 30000 21199 70.66% 4099 13.66% 5438 18.13%

63 30000 25246 84.15% 14565 48.55% 15044 50.15%

64 30000 21345 71.15% 6798 22.66% 7123 23.74%

65 30000 26360 87.87% 12756 42.52% 12418 41.39%

66 30000 25127 83.76% 7322 24.41% 7945 26.48%

67 30000 25516 85.05% 12592 41.97% 13744 45.81%

68 30000 22195 73.98% 8978 29.93% 10223 34.08%

69 30000 13988 46.63% 2954 9.85% 2561 8.54%

70 30000 19108 63.69% 6608 22.03% 6541 21.80%

71 30000 30000 100.00% 20343 67.81% 20384 67.95%

72 30000 25530 85.10% 7316 24.39% 9532 31.77%

73 30000 18663 62.21% 4247 14.16% 2498 8.33%

74 30000 21774 72.58% 7489 24.96% 7316 24.39%

75 30000 24960 83.20% 11665 38.88% 10427 34.76%

76 30000 24551 81.84% 15770 52.57% 13924 46.41%

77 30000 19673 65.58% 7991 26.64% 7621 25.40%

78 30000 19984 66.61% 17960 59.87% 18172 60.57%

79 30000 22362 74.54% 8711 29.04% 10905 36.35%

80 30000 18174 60.58% 10205 34.02% 10702 35.67%

81 30000 27435 91.45% 8601 28.67% 14130 47.10%

82 30000 23562 78.54% 12285 40.95% 11983 39.94%

83 30000 26001 86.67% 12742 42.47% 16316 54.39%

84 30000 22357 74.52% 13057 43.52% 12589 41.96%

85 30000 24237 80.79% 9640 32.13% 7319 24.40%

86 30000 26622 88.74% 9262 30.87% 12646 42.15%

87 30000 21145 70.48% 13549 45.16% 13765 45.88%

88 30000 24889 82.96% 11566 38.55% 13607 45.36%

89 30000 25947 86.49% 16470 54.90% 14853 49.51%

90 30000 22297 74.32% 7357 24.52% 9508 31.69%

91 30000 20130 67.10% 4641 15.47% 4151 13.84%

92 30000 20438 68.13% 7199 24.00% 8354 27.85%

93 30000 18162 60.54% 2634 8.78% 3551 11.84%

94 30000 18322 61.07% 10931 36.44% 12971 43.24%

95 30000 20778 69.26% 7202 24.01% 6089 20.30%

96 30000 25270 84.23% 11733 39.11% 12030 40.10%

97 30000 23960 79.87% 10908 36.36% 10886 36.29%

98 30000 20168 67.23% 10980 36.60% 12764 42.55%

99 30000 22662 75.54% 12699 42.33% 15152 50.51%

100 30000 19755 65.85% 11578 38.59% 10999 36.66%

mean 22232.97 74.11% 9651.19 32.17% 10101.54 33.67%

STD 3292.854 10.98% 3909.051 13.03% 4225.339 14.08%

Table I. Comparison of received packets at base station (average of 100 networks randomly

deployed)

Trial PBS_NC PBS_WC1 WC1

Improvement PBS_WC2

WC2

Improvement

1 214 265 23.83% 246 14.95%

2 63 114 80.95% 95 50.79%

3 96 94 -2.08% 94 -2.08%

4 72 205 184.72% 206 186.11%

5 117 151 29.06% 161 37.61%

6 162 217 33.95% 224 38.27%

7 203 353 73.89% 354 74.38%

8 141 216 53.19% 229 62.41%

9 181 286 58.01% 268 48.07%

10 279 314 12.54% 330 18.28%

11 149 374 151.01% 374 151.01%

12 157 243 54.78% 203 29.30%

13 143 279 95.10% 253 76.92%

14 66 206 212.12% 205 210.61%

15 218 269 23.39% 262 20.18%

16 262 364 38.93% 361 37.79%

17 352 430 22.16% 406 15.34%

18 217 317 46.08% 317 46.08%

19 173 279 61.27% 282 63.01%

20 172 308 79.07% 312 81.40%

21 198 290 46.46% 309 56.06%

22 75 256 241.33% 224 198.67%

23 227 320 40.97% 309 36.12%

24 207 314 51.69% 304 46.86%

25 99 293 195.96% 279 181.82%

26 153 208 35.95% 231 50.98%

27 84 256 204.76% 233 177.38%

28 62 155 150.00% 155 150.00%

29 275 256 -6.91% 243 -11.64%

30 233 282 21.03% 287 23.18%

31 202 293 45.05% 315 55.94%

32 60 158 163.33% 162 170.00%

33 71 199 180.28% 217 205.63%

34 99 220 122.22% 214 116.16%

35 183 318 73.77% 304 66.12%

36 102 244 139.22% 246 141.18%

37 62 196 216.13% 193 211.29%

38 181 336 85.64% 345 90.61%

39 155 200 29.03% 193 24.52%

40 150 217 44.67% 230 53.33%

41 192 231 20.31% 249 29.69%

42 120 166 38.33% 203 69.17%

43 70 220 214.29% 205 192.86%

44 109 129 18.35% 122 11.93%

45 238 332 39.50% 341 43.28%

46 260 346 33.08% 371 42.69%

47 158 221 39.87% 219 38.61%

48 206 312 51.46% 327 58.74%

49 113 213 88.50% 212 87.61%

50 127 213 67.72% 224 76.38%

51 212 306 44.34% 316 49.06%

52 46 135 193.48% 128 178.26%

53 220 260 18.18% 287 30.45%

54 115 173 50.43% 113 -1.74%

55 149 232 55.70% 246 65.10%

56 186 308 65.59% 347 86.56%

57 0 267 Infinity 262 Infinity

58 132 250 89.39% 262 98.48%

59 186 304 63.44% 308 65.59%

60 113 235 107.96% 225 99.12%

61 198 283 42.93% 274 38.38%

62 286 359 25.52% 376 31.47%

63 116 174 50.00% 175 50.86%

64 175 272 55.43% 259 48.00%

65 88 163 85.23% 169 92.05%

66 80 323 303.75% 336 320.00%

67 118 168 42.37% 166 40.68%

68 147 189 28.57% 169 14.97%

69 348 497 42.82% 502 44.25%

70 219 230 5.02% 208 -5.02%

71 0 101 Infinity 101 Infinity

72 58 256 341.38% 238 310.34%

73 302 363 20.20% 405 34.11%

74 131 213 62.60% 233 77.86%

75 150 209 39.33% 220 46.67%

76 160 199 24.38% 232 45.00%

77 172 306 77.91% 318 84.88%

78 142 142 0.00% 141 -0.70%

79 130 155 19.23% 132 1.54%

80 200 279 39.50% 253 26.50%

81 90 179 98.89% 144 60.00%

82 127 117 -7.87% 126 -0.79%

83 57 172 201.75% 137 140.35%

84 167 214 28.14% 219 31.14%

85 121 284 134.71% 280 131.40%

86 144 224 55.56% 208 44.44%

87 249 336 34.94% 325 30.52%

88 134 217 61.94% 210 56.72%

89 39 169 333.33% 185 374.36%

90 196 251 28.06% 243 23.98%

91 205 305 48.78% 329 60.49%

92 302 390 29.14% 408 35.10%

93 299 486 62.54% 481 60.87%

94 258 236 -8.53% 226 -12.40%

95 175 254 45.14% 250 42.86%

96 100 206 106.00% 231 131.00%

97 85 218 156.47% 218 156.47%

98 148 206 39.19% 206 39.19%

99 155 228 47.10% 211 36.13%

100 214 306 42.99% 291 35.98%

mean 157.52 250.27 77.11% 249.77 75.57%

STD 72.53901 76.65268 73.08% 80.62143 72.12%

Table II. Comparison of energy leftover of the whole network (average of 100 networks

randomly deployed)